Working Paper Series
Erik Frohm, Vanessa Gunnella
Sectoral interlinkages in
global value chains:
Spillovers and network effects
No 2064 / May 2017
Disclaimer: This paper should not be reported as representing the views of the European Central Bank
(ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB.
Abstract
This paper studies the role of global input-output linkages in transmitting economic
disturbances in the international economy. Our empirical results suggest that these
sectoral spillovers are both statistically signicant and of economic importance. We
also provide evidence that it is not the interlinkages per se that matter for the international transmission but rather the presence of global hub sectors that are either large
suppliers or purchasers of other sectors' inputs. When the links between these sectors
and the rest of the global value chain are severed, the spillovers diminish strongly
and eventually become statistically insignicant. This highlights the importance of
the structure of the network for enabling spillovers and the prominent role played by
hub sectors in the global economy.
JEL Classication E30, E32, F44, F62
Keywords input-output linkages, networks, spillovers, global value chains.
ECB Working Paper 2064, May 2017
1
Non-technical summary
Decades of rapid globalisation have turned national production structures into complex
global value chains. In these international networks, rms purchase inputs from suppliers,
add value and sell them onward to other rms or nal consumers. These value chains are
intricate and involve companies across various sectors in dierent countries.
We show that the structure of global input-output linkages matters for how economic
disturbances are transmitted through sectors in the world economy. Our empirical estimates suggest that a 1% change in real value added in the global value chain translates
into around 0.3 percentage point impact on the real value added of a sector, on average.
These eects are robust to the inclusion of various controls, such as other country-sectorspecic determinants of real value added, movements in aggregate economic activity in the
national economy, global factors (commodity prices and global interest rates) and unobserved common factors.
This paper also provides evidence that it is not the production linkages per se that
cause the spillovers. Instead, they are largely driven by a few global hub sectors that
link otherwise unrelated sectors together. In our dataset, the top 10 upstream sectors
barely changed between 1997 and 2009 and comprise primarily "renting of machinery and
equipment and other business activities" (which apart from renting comprise of research
and development and computer related activities) and raw materials (chemicals, mining
and metals) in the United States, Germany and Russia. Downstream in the value chain,
sectors in China have risen to prominence. From not even entering the top 20 in 1997, the
construction, basic metals and electrical and optical equipment sectors in China occupy
the top 10 ranking in 2009.
When we sever the links between the top global hub sectors and the rest of the value
chain spillovers are considerably reduced and eventually become statistically insignicant. This highlights the importance of the structure of the global network for generating
spillovers and the prominent role played by hub sectors in the global economy. Our results thus add to the growing empirical literature on the quantitative importance of global
input-output linkages for movements in aggregate activity.
ECB Working Paper 2064, May 2017
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1
Introduction
National economies are made up of complex production networks. Firms purchase inputs
from upstream suppliers, add value, and sell intermediate inputs to other downstream rms
that add value before the product or service is sold for nal consumption. Decades of rapid
globalisation have turned national production networks into global value chains that involve
rms in dierent countries and across many dierent sectors (Baldwin, 2006; 2016). The
structure of international production networks matters. As a recent strand of research has
shown, shocks to individual rms or sectors that propagate through production linkages
can be one explanation for the origins of aggregate movements in economic activity (Long
and Plosser, 1983; Horvath, 1998, 2000; Foerster, Sarte and Watson, 2011; Jones, 2011 and
Acemoglu, Carvalho, Ozdaglar and Tahbaz-Salehi, 2012).
While a sector's contribution to total value added is the purely accounting reason
for why some sectors might have a disproportionately large impact on economic activity
in the aggregate, it is not the only factor that makes them a - in the network jargon
- "critical node". Their potential for propagating shocks depend both on the degree to
which they are supplying or purchasing inputs to/from other sectors and how they shorten
the distance between sectors that do not otherwise trade directly (Acemoglu, Carvalho,
Ozdaglar and Tahbaz-Salehi, 2012; Carvalho, 2014 and Pesaran and Yang, 2016). As
is argued by this literature, and as we emphasise in the rest of this paper, the network
structure of global production, and in particular the presence of global hub sectors, is one
important explanation for why and how economic activity spills over through sectors and
across countries.
These insights have profound implications for today interconnected world. Could the
rather spontaneous organisation of rms into global value chains be a candidate for the
transmission of economic disturbances throughout the world economy and help explain
why business cycles across countries are increasingly synchronised (Frankel and Rose, 1998;
Burstein, Kurz and Tesar, 2008 and di Giovanni and Levchenko, 2010)?
To shed light on these questions, we draw on, and contribute to, two strands of the
literature: (i) the role of input-output linkages and production networks for transmitting
economic activity across sectors in dierent countries and (ii), the emergence of global value
chains in international trade and the role of cross-border production for synchronising
activity across countries. We make use of global input-output data from the publicly-
ECB Working Paper 2064, May 2017
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available World Input-Output Database. These tables contain entries for 35 sectors in
40 countries annually, over 17 years (from 1995 to 2011) and cover around 85% of world
GDP1 .
In order to test for real value added spillovers across sectors in the global economy,
we specify a non-linear panel data model following Kapetanios, Mitchell and Shin (2014).
The model allow us to estimate upstream and downstream network eects from a group
of endogenously determined sectors in the (global) value chain and for controlling for
other observed and unobserved causes of a sector's real value added, as well as other
determinants. Through our threshold estimation we are also able to determine which are
the sectors driving the transmission across countries ("hub" sectors).
Our results conrm that trade in global value chains and in particular global hub sectors
has made international production tightly interconnected over time. Empirical estimates
from our econometric model suggest that a 1% change in real value added in the global
value chain of a sector translates into around 0.3% impact on a sector, on average.
The primary reason for the spillovers is, according to our results, the presence of global
hub sectors that either act as large suppliers of inputs from - or users of - inputs of many
others. The hubs in the global network have changed over time, primarily downstream in
the value chain. Here, we can in particular observe the increasing importance of China in
our data. From not even entering the top 20 of the most important sectors in 1997, three
Chinese sectors (construction, electrical and optical equipment and basic and fabricated
metals) appear in the top 10 in 2009. Upstream in the value chain, our model suggests
that the 10 most important sectors have remained broadly stable between 1997-09 and are
dominated by "renting of machinery and equipment and other business activities", which
includes R&D and computer activities, raw materials, chemicals and nance in the United
States, Germany and Russia.
To illustrate the importance of these hubs for generating spillovers, we perform a
counter-factual exercise where the links between the hubs and the rest of the global production network are severed. Once we have severed the linkages one by one, the eects
through the global value chains diminish rapidly. Specically, when the links between the
top 15 hubs (three upstream and 12 downstream sectors) and the rest of the global value
1 Timmer,
M. P., Dietzenbacher, E., Los, B., Stehrer, R. and de Vries, G. J. (2015), An Illustrated
User Guide to the World Input-Output Database: the Case of Global Automotive Production. Review of
International Economics, 23: 575-605. doi:10.1111/roie.12178
ECB Working Paper 2064, May 2017
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chain have been removed, the spillovers become statistically insignicant. This indicates
that global hub sectors have a key role to play in synchronising sectoral economic activity
within and across countries and provides empirical evidence for the theoretical analysis
outlined by Acemoglu, Carvalho, Ozdaglar and Tahbaz-Salehi (2012). Moreover, akin to
Acemoglu, Akcigit and Kerr (2015), we also assess the direction of two exogenous shocks
("upstream" or "downstream" in the global value chain) and nd evidence of backward
propagation of a demand shock.
The rest of this paper is organised as follows: Section 2 starts with a brief description
of the literature related to this paper. Section 3 presents the main data sources and some
stylized facts about the global input-output network. Section 4 introduces the empirical
specication and Section 5 presents the empirical estimates of real value added spillovers
and shock transmission in global value chains as well as illustrating some post-regression
evidence supporting the importance of hubs. Section 6 provides some concluding remarks
and avenues for future research.
2
Related literature
This paper is related to two dierent strands of the literature: (i) the role of input-output
linkages for economic activity across sectors and (ii) the emergence of global value chains
in international trade and the role of cross-border production for synchronising activity
across countries. In the following, we will provide a brief overview of this literature.
2.1
Production networks and spillovers
Starting with the seminal work of Long and Plosser (1983), a growing literature on the role
of sectoral input-output linkages for movements in aggregate activity has emerged (Horvath, 1998, 2000; Foerster, Sarte and Watson, 2011; Jones, 2011 and Acemoglu, Carvalho,
Ozdaglar and Tahbaz-Salehi, 2012). Their ndings suggest that idiosyncratic microeconomic shocks that propagate through rm or sectoral interlinkages within an economy could
help explain the origins of aggregate uctuations. Specically, Horvath (1998) showed that
as much as four fths of volatility in United States real GDP could be due to independent
shocks to various economic sectors, while Foerster, Sarte and Watson (2011), estimates that
idiosyncratic sectoral shocks explain about half of the variability in industrial production
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in the United States after the mid-1980s. Similarly, Atalay (2014) nd that around two
thirds of variability in aggregate output could be due to sector-specic shocks that spread
through input-output linkages, in a model where incomplete substitutability among inputs
is assumed. Moreover, Carvalho (2014) argues that, in particular, the presence of large
sectoral hubs in production networks facilitates the propagation of shocks of otherwise
localised disturbances. Not only do these hubs have direct connections with many other
sectors through supply and use relationships, they also bring otherwise unrelated sectors
"closer" to each other in a network sense.
Empirical evidence on how economic disturbances transmit across input-output linkages
is sparser, but recent strides have been made, in particular by Saito, Nirei and Carvalho
(2014), di Giovanni, Levchenko and Mejean (2014), Acemoglu, Akcigit and Kerr (2015)
and across countries by Boehm, Flaaen, Pandalai-Nayar, (2014).
These empirical ndings are somewhat in contrast to much of the standard macroeconomic literature, starting with Lucas (1977). There, it is argued that idiosyncratic shocks
to individual rms or sectors will have very little - if any - impact on economic activity in
the aggregate. When the economy is disaggregated enough, the argument goes, a shock
to one sector will be broadly oset by a shock of the opposite sign to another sector and
in the aggregate, these idiosyncratic sector shocks will tend to "average out". However, as
Gabaix (2011) showed, when an economy's rm-size distribution is "fat-tailed", idiosyncratic shocks to very large rms may not be negated by shocks of the opposite sign to
smaller rms and could thus translate into macroeconomic uctuations. Acemoglu, Carvalho, Ozdaglar and Tahbaz-Salehi (2012) expanded on this idea, and showed that not only
does the rm-size distribution matter, but also the structure of the input-output network.
For example, if the economy consists of n number of sectors that do not sell or buy
intermediate inputs from each other (Figure 1), Lucas diversication argument will hold as
n increases and any idiosyncratic shock to one sector will be broadly oset by a shock of the
opposite sign to other sectors. Similarly, in an equally dependent network where each sector
is symmetrically selling and purchasing inputs from all other sectors, the diversication
argument will also hold as n increases. However, if the economy is more similar to the
third type of network (a so-called star-network) where one sector is disproportionately a
large supplier (or purchaser) of inputs to all other sectors, shocks may not average out,
even if n increases. This theoretical reasoning is crucial for the analysis in this paper and
we will dedicate Section 3 to present some empirical facts about the presence of sectoral
ECB Working Paper 2064, May 2017
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hubs in the global input-output network.
2.2
Global value chains and co-movements in business cycles
Although national production links are important, the build-up of global production networks following decades of continuous globalisation has increased the interaction among
sectors across countries. Baldwin (2006) characterised this transformation of international
trade over time as two unbundlings. This rst enabled the spatial separation of production
from consumption, as transportation costs fell. The second unbundling gave rise to what
we today call trade in global value chains and permitted the scattering of production stages
across countries due to the sharp fall in communication and coordination costs2 .
If links between sectors could aect aggregate activity in a particular country, could it
be that trade between sectors in global value chains also helps to explain the increasing
synchronisation of business cycles across countries, as documented by Frankel and Rose
(1998)? As standard international business cycle models have been unable to account
for these empirical ndings, this has given rise to what Kose and Yi (2006) dubbed the
"trade co-movement puzzle". Both Burstein, Kurz and Tesar (2008) and di Giovanni and
Levchenko (2010) provides insights into this puzzle by documenting higher business cycle
correlations among pairs of sectors that use each other as intermediate inputs, suggesting
that "production sharing" is one signicant part in explaining the puzzle.3 Moreover, di
Giovanni, Levchenko and Méjean (2014) show that business cycle shocks transmit through
direct trade and indirect linkages by large multinational rms. In the absence of those linkages, average business cycle correlations fall signicantly and emphasise the role played by
fragmented production for explaining synchronisation of economic activity across countries.
2.3
The contribution of this paper
This paper adds to the empirical evidence of sectoral input-output spillovers in (global)
production networks. Previous empirical work that has assessed the importance of inputoutput linkages has focused mainly on national input-output links, usually at one point in
time (see for example Acemoglu, Akcigit and Kerr, 2015). We improve on this literature
2 For
an explanation of why rms organise in global value chains, see for instance Antràs and Chor
(2013)
3 Others, for example Imbs (2004) argued that co-movement in business cycles could simply be a reection of the fact that country-pairs that trade with each other are simply similar in other ways and thus
subject to common shocks.
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in two respects: rst, we do not only take into account national production structures,
but truly global interlinkages with data from the World Input-Output tables4 . This is
important as production is not only a national matter in the age of global value chains.
Second, we allow for the structure of the network to vary over time, in order to account
for structural changes in the global economy such as the growing importance of trade in
services and the rise of China in trade.
Moreover, our econometric strategy allows us to endogenously determine the most relevant sectors in the global input-output network, the so-called hubs. In this setting, only
the sectors above a certain threshold enter into the function determining spillovers on other
sectors. With this information, we can pinpoint the globally most important sectors (those
which most often enter the function of all other sectors) both as upstream suppliers and
downstream users. Once identied, we conduct a counterfactual exercise where the links
between these sectors and the other sectors in the network are severed, one by one. This
enables us to test whether or not the structure of the network is instrumental for transmitting economic activity, as proposed by Acemoglu, Carvalho, Ozdaglar and Tahbaz-Salehi
(2012). Moreover and in a similar vein to Acemoglu, Akcigit and Kerr (2015), we also test
the magnitude and direction of two exogenous shocks, one to demand (government spending) and one to supply (TFP). This exercise illustrates the direction of shock propagation
in the network (upstream and downstream).
3
3.1
Data and stylised facts
Data sources
In the rest of this paper, we use a sectoral dataset constructed from the publicly available
World Input Output Database (WIOD). These global input-output tables contain annual
information for 35 sectors, comprising primary, durable and nondurable manufacturing as
well as services sectors, including nancial intermediation. The tables are available for
40 countries, of which a majority is in the European Union, but also include countries in
North America, South America and Asia, as well as the rest of the world (constructed
as one economy) from 1995 to 2011. Therefore, for each year a full country-sector inputoutput matrix of the dimension 1435 × 1435 is available and allows for the analysis of
4 Global input-output tables have also been used by Auer, Levchenko and Sauré (2017) who investigate
ination spillovers through input linkages.
ECB Working Paper 2064, May 2017
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supply and use relationships between a sector in a specic country and all other sectors in
the country as well as all sectors in the 39 other countries.5
These tables are accompanied by Socio-Economic Accounts which contain countrysector panel data on employment (number of workers, compensation and share of labour in
high, medium and low skilled occupations), capital stocks, gross output and value added
at current (until 2011) and constant prices (until 2009).6
The two data-sets form the basis for the network-based measures constructed in the
following and enable the complete mapping of supply and use relationships in the global
economy, which will be taken advantage of in Section 4. For further computational details,
the reader is referred to Appendix B.
3.2
Network structure of the global economy
As argued by Acemoglu, Carvalho, Ozdaglar and Tahbaz-Salehi (2012), the structure of
production networks matters for if - and how - shocks propagate and if they could lead
to aggregate uctuations. To illustrate the network structure of the global economy, we
provide some stylised facts and show that the data in the World Input-Output tables are
indeed characterised by some large sectoral hubs.
We compute the weighted degree dened as di =
PN
j=1
wij , that is the sum of all
weights of all links attached to a sector i for each country-sector pair in the network (see
also Carvalho, 2014 and Cerina, Zhu, Chessa and Riccaboni, 2015). This measure captures
sector i's connectivity through (binary) supply and use relationships but also the strength
of these relationships (the monetary value). In other words, it assigns a larger value to
sectors supplying/purchasing inputs of many other sectors in the network, while it assigns
a value equal to zero if there are no interlinkages. If the global production network was
fairly equally distributed (recall the middle illustration in Figure 1) the measure would
simply yield a horizontal line across all sectors. If the network is characterised by hubs
and more similar to a star network as in Figure 1, we would expect to see a left-skew in
the distribution of sectors, meaning that a small number of sectors have relatively strong
input supplying/purchasing relationships with many other sectors in the network.
Figure 2 shows the weighted degree across all country-sectors in 2009. Given the level
5 www.wiod.org
6 For the construction of the World Input-Output tables, see Dietzenbacher, E., Los, B., Stehrer, R.,
Timmer, M. and De Vries, G., 2013. The construction of world input-output tables in the WIOD project.
Economic Systems Research, 25(1), pp.71-98.
ECB Working Paper 2064, May 2017
9
of aggregation in the World Input-Output tables, very few sectors have no connection
whatsoever to other sectors (the ones that do, are largely private households with employed
persons). The average weighted total degree across sectors is 0.9 and around that value
we nd for example pulp and paper in Italy and France, electricity gas and water supply
in the UK, and chemicals and chemical products in Canada.
Above the 95th percentile of the weighted degree, we nd large input supplying/purchasing
sectors such as nancial intermediation in the United States and the United Kingdom, renting of machinery and equipment and other business activities in the United States, France
and Italy and mining and quarrying in Russia as well as wholesale trade in the United
States and China.
One could argue that the weighted degree is simply a reection of a sector's share of
global value added. If so, could movements in these disproportionately large sectors be
the purely accounting reason as to why sectoral activity might impact aggregate activity?
While there is some correlation between a sector's contribution to global value added and
its total degree, it is not the full story (Figure 3). For example, about 22% of sectors above
the 95th percentile in terms of total degree have very low shares of global value added (less
than 0.01%). These sectors are typically mining and quarrying activities in Europe, Russia
and Asia and renting of machinery and equipment and other business activities in Western
and Eastern Europe.
Another way of documenting the presence of hub sectors is to plot the evolution of the
"distance" between any pair of sectors over time7 . Distance measures the shortest path
between any two sectors in the network, that is, how many times inputs from one sector
are sold in order to reach another sector. If the network is characterised by hubs, distance
should be lower than in the absence of them. One could think of an economy which has
one large hub sector (similar to the star network in Figure 1) and another network which
is less integrated. In the star network, each sector is only one trade away from each other
through the hub. In less integrated networks, inputs from one sector travel further so the
network distance is larger.
The blue line in Figure 4 (left-hand panel) shows the average distance across pairs of
domestic sectors with foreign sectors in the World Input-Output tables. It is evident that
network distance has fallen since the 2000s, albeit with a short disruption and a slowdown
following the Great Recession. If we focus on sectors in specic countries, we can see
7 Here,
the shortest path is computed with the Dijkstra algorithm.
ECB Working Paper 2064, May 2017
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that their distance to other countries have generally become smaller over time. This is
particularly noticeable for China, whereas the declines in the United States and Germany
have been more gradual. Sectors in Germany have on average had lower distance to foreign
sectors during the whole period, highlighting the relative openness of the German economy.
What would be the implications of the increasing presence of hubs in the network? Since
they shorten the distance between otherwise unrelated sectors, we would expect correlation
of economic activity between sectors on average to be higher as distance falls (Carvalho,
2014). To illustrate this point, we compute average pairwise correlations of sectoral real
value added growth over 1995-2009 for all country-sectors and across various distances upand downstream in global network in Figure 4 (right-hand panel).
Indeed, economic activity between two sectors correlates more strongly when distance is
lower. This is important, because we argue that not only do hubs cause spillovers because
they are large suppliers or purchasers of inputs, but they also shorten the distance between
otherwise unconnected sectors. This could also help explain why activity across sectors comoves within a country, but also across countries, even without the presence of aggregate
shocks. Another interesting question is whether we can observe a co-movement in the gross
output growth of sectors driven by network interdependence.
The Moran's I statistic provides a measure of correlation of a variable of interest through
network relations and is dened as:
n
I=P P
i
P P
i
j
wij
j
wij (yi − ȳ)(yj − ȳ)
P
2
i (yi − ȳ)
When we test the hypothesis of no network interdependence (I = 0), we nd that for
almost all the years in the sample we strongly reject the null hypothesis, meaning that
we nd evidence for positive network interdependence of gross output growth (Table 1).
In sum, the network structure of the data in the World Input-Output tables seems to be
characterised by sectoral hubs, and over time there has been a clear evolution towards
tighter economic integration globally, even though most supply chains have clear regional
characteristics (WTO 2013). Now, the relevant question is whether we can statistically
establish an economically signicant relationship between activity within a given sector
and activity in its global value chain.
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4
Methodology
To investigate how sectoral real value added spills over in global value chains, we utilise
an econometric non-linear panel data model proposed by Kapetanios, Mitchell and Shin
(2014). In this model, the current economic activity of a sector in a country, say sector
i, is determined by sector i's past activity and a weighted average of the past economic
activity of a group of sectors involved in its (global) value chain. In addition, we also
consider network distance of other sectors from sector i. In this setting, more weight is
attributed to sectors which have a higher share of value added in sector i's production and
have a shorter distance to sector i in the World Input Output network. In the production
of a car, for example, we would attribute more weight to the sector producing tires in the
nished car's reference group, not only because the tires contribute to the nished car's
total value added but also because the tires industry directly sells intermediate inputs to
the car industry. Consider the following model specication:
up
down
yit = ηt + ρlag yi,t−1 + ρup ỹi,t−1
+ ρdown ỹi,t−1
(1)
where yit is activity in a sector i at time t, ỹ up is the upstream value added of other sectors
dened by:
up
ỹi,t−1
=
X
up
up
1(wij,t−1
≥ rup )wij,t−1
yj,t−1
(2)
j6=i
down
is the downstream value added of other sectors dened by:
yi,t−1
down
ỹi,t−1
=
X
down
down
1(wij,t−1
≥ rdown )wij,t−1
yj,t−1
(3)
j6=i
In the weights' denition, we take both value added contribution and distance into account:
up
wij,t
=
down
wij,t
=
V Aj→i,t
1
× up
V A∗→i,t dij,t
(4)
V Ai→j,t
1
× down
V Ai→∗,t dij,t
(5)
where VA is value added contribution to total output, i.e. the value added provided by
a sector to another sector's total production, and d is the shortest distance between two
sectors. Through the Leontief insight, we are able to trace the gross output used in all
ECB Working Paper 2064, May 2017
12
intermediate stages of production. Therefore, VA in (4) and (5) takes into consideration
not only the direct connection via each sector's production chain, but also second and
higher order interconnections to other sectors via direct trading partners.8 The inclusion
of both the value added share of a sector's total purchases (4) or sales (5) and the distance
metric intends to achieve that the rst component captures an importance of other sectors
in sector i's production process and the second component captures the eective trading
relationship between the sector i and other sectors. As we have shown previously, network
distance is important because, apart from the value added contribution, whether sector j
is directly trading with sector i or through some intermediate steps involving other sectors
is relevant to degree in which activity in the two sectors correlate.9 Table 5 in the appendix
shows that the upstream and downstream measures do indeed capture dierent relations
among sectors.
This panel model allows us to control for observed and unobserved common factors
which could cause activity growth in a sector, but that is not driven by spillovers through
production linkages. Therefore, the estimated spillover coecient will just pick up the
inuence of the global value chain on activity of sector i. In the regression, we also include
a k × 1 vector of sector, country or global variables, xi,t , a full set of year eects ηt and the
error term has the form:
εit = λ0 ft + uit
where ft is the f × 1 vector of unobserved common factors modelled as in Pesaran (2006),
i.e. with the cross-sectional averages of the dependent variable and the regressors and uit
is an iid error process.
Apart from better controlling for observed and unobserved factors driving uctuations
in economic activity, another interesting novelty of this approach is that it allows for the
endogenous determination of the most important sectors in the global network (the so
called hubs). The threshold search identies the parameters rup and rdown which are then
8 Algebraically, V A
j→i,t is an entry of the matrix V At = vt Lt GOt where vt is a (N C ∗ N I × N C ∗ N I)
diagonal matrix with value added vector on the diagonal, Lt is the Leontief matrix (N C ∗ N I × N C ∗ N I)
and GOt is a (N C ∗ N I × N C ∗ N I) diagonal matrix with gross output on the diagonal. N C is the
total number of countries and N I is the total number of sectors. The Leontief matrix is computed as
Lt = (I − At )(−1) , with the dimension (N C ∗ N I × N C ∗ N I), where I is the identity matrix and At is the
(N C ∗ N I × N C ∗ N I) technical coecient matrix, that is the use of intermediate goods in the production
of one unit of output and it is computed from the global input-output matrix Zt as At = Zt GOt(−1) .
9 We also estimated the model with weights not adjusted by the distance variable. The model delivers
similar results, however it has a higher sum of squared errors.
ECB Working Paper 2064, May 2017
13
used to choose which sectors are included in (2) and (3).10 These hubs will be identied in
a regression context as those sectors entering most often into the endogenously determined
group of relevant sectors across all sectors in the global network.
The threshold obtained from the grid search minimises the sum of squared errors, and
thus ensure that the nal model best ts the data. In a network sense, our approach
identies the signicant edges ("links") between nodes. This makes it possible to draw
up ex-post a rank of sectors for each year, according to their prominence in the global
production network. It is worth noting that we identify the hubs as those sectors with
the highest weights for the partners and we evaluate the importance of a sector with its
connectedness (number of links). After all, by using only a sector's degree as measure of
its importance a sector may appear important just because it provides a very high share
of inputs to a few sectors even when it is not linked to many other sectors.
5
Results
In order to empirically estimate real value added spillovers through a sector's global value
chain, we utilise our econometric model described in Section 4. We also discuss the results
and provide some post-estimation details.
5.1
Estimates of the spillovers
We consider log-changes of the variables involved in the estimation, in order to address
stationarity concerns regarding macroeconomic time series and also attenuate Nickell's
bias11 . The results from the regressions are reported in Table 2. The baseline regression
only includes a lagged dependent variable and the past economic activity of upstream
and downstream sectors' in the global value chain. As a robustness-check of the results,
we also add other determinants such as time dummies and country and sector-level controls. Specically, the regressions include country aggregate real value added, sector-level
employment and global factors such as prices of agricultural products, metals and fuels as
well as global interest rates. We also run regressions including capital stocks for the sample
10 The
up
threshold parameters are determined with a grid search over several percentile values of wij,t
and
down
up down
wij,t . (r , r
) is the combination minimizing the model's sum of squared errors as in Hansen (1999).
11 Nickell's bias (1981) occurs in dynamic panel data with xed eects and is particularly severe when
the number of cross-sectional units is considerably greater than the number of time observations.
ECB Working Paper 2064, May 2017
14
1997-2007, which also veries the consistency of the results for the pre-crisis period.12
The spillovers through the global value chain are signicant and the magnitudes are
notably relevant. The addition of control variables reduces the fairly large coecients but
does not compromise their signicance. A 1% change in real value added in the global
network translates into an impact of slightly above 0.3%13 to a sector's real value added
growth, on average. This means that aggregate eects do play a role in driving aggregate
uctuations, but they are not the only source and economic activity is also aected by
sector-level production linkages.
5.2
Hubs in the global value chain
With the estimates derived from equation (1) and in particular the threshold parameters
rup and rdown 14 we are now able to determine, for each year, the sectors entering the
reference group of each sector i in the sample. This enables us to identify upstream and
downstream hubs in the global production network as those sectors entering the highest
number of times in other sectors' upstream and downstream groups, respectively. Table
3 shows the rankings of sectors derived from the regressions that produced the results in
Table 2 for 1997 and 2009. Looking at the upstream ranking, the top sectors are active
in "renting of machinery and equipment and other business activities" (which includes
R&D and computer activities) and raw materials (chemical, mining, metals) in the United
States, Germany and Russia. This result is fairly intuitive and we expect such sectors to
be located upstream as they provide primary inputs (both R&D and raw materials) to
the production processes of many other sectors. This ranking changed little over time. As
regards sectors situated downstream the production network, the ranking is dominated by
manufacturing (cars, machinery and electrical and optical equipment), construction and
government activities (in the United States).
Interestingly, in the top 10 downstream ranking we can observe the rise to prominence
of some Chinese sectors at the expenses of those in the United States in recent years: three
sectors in the United States have been replaced by three Chinese sectors, highlighting the
growing importance of China in global value chains. The regression including sector level
12 Tables
7 and 8 in Appendix A report the standardized and non-standardized results for the regression
including the capital variable for the sample 1997-2007.
13 The estimate refers to coecients obtained from the regression with non-standardized variables (see
Table 6 in the Appendix).
14 The reader can refer to footnote 10 for details about the threshold determination.
ECB Working Paper 2064, May 2017
15
capital stocks delivers the same ranking.
5.3
Estimates of spillovers stemming from two hub sectors
Another illustrative result of sectoral spillovers can be constructed by using the estimated
coecients ρup and ρdown and the weights assigned to each sector pair i, j . In Table 4, we
consider changes in real value added in one upstream and one downstream sector and their
impact on all other sectors in the production network, stemming from all supply and use
relations. We consider the top 1 upstream sector in 2009, German "renting of machinery
and equipment and other business activities". A 1% change in real value added in this
sector would aect 321 other sectors (almost a fourth of all sectors in our data) and the
spillovers to other sectors would amount to 1.14%. About half of this impact is on other
sectors in Germany, and slightly less than half is transmitted to other sectors in the euro
area. The remainder (almost 16%) aect sectors in other parts of the world. Interestingly,
the spillovers amplify through the production network.
For the downstream impacts we utilise a sector which has become prominent as a nal
assembler in many global value chains during the 2000s, namely China's electrical and
optical equipment sector.15 According to our estimates, a 1% change to real value added
in this sector would have impact on 13% of all sectors in the data and would cause real
value added spillovers of 0.47 percentage points. It is interesting to note that almost two
thirds of the eect concern sectors in other countries than China.16
5.4
Spillovers in the absence of hub sectors
The importance of the sectoral hubs in the global network can be illustrated when the
input-output relations between them and the rest of the global value chain are severed.
This counter-factual exercise has two interesting features: rst, if the hubs are instrumental
in transmitting economic disturbances we would expect to see falling size of the estimated
coecients on the up- and downstream spillovers as hubs are gradually removed. Second,
we would expect the spillovers to become statistically insignicant when enough top hub
sectors are removed. We utilise the full rankings of sectors derived in Table 3 to rst
identify the hubs and then re-estimate equation (1) when the ties for these sectors are
15 See
for example, Lu (2015).
estimated spillover eects for the model with sector-level capital stocks and the 1997-2007 sample
are reported in Table 9 in Appendix A.
16 The
ECB Working Paper 2064, May 2017
16
severed, one at a time. This is done by setting the weight in (4) and (5) equal to zero rst
for the top one hub sector, then the top two, then three, and so on. The process continues
until the estimated spillovers through the global value chain are statistically insignicant.
These recursive estimates reveal the importance of the global hub sectors for real value
added spillovers (Figure 5). When the top ve upstream and downstream global sectors
are cancelled (ten in total), spillovers through the global value chain fall by almost a fth.
When the top three upstream and the 12 downstream global sectors are removed, spillovers
through the global value chain become statistically insignicant and this highlights the
importance of large global hubs in transmitting economic activity across sectors in dierent
countries.
5.5
Transmission of sectoral shocks
Following Acemoglu, Akcigit and Kerr (2015), we also test the direction of two plausibly
exogenous shocks. We consider one demand shock (government spending) and one supply
shock (to total factor productivity). According to a theoretical setup in which production
and preferences is Cobb-Douglas, supply shocks should propagate from upstream sectors
to those downward in the supply chain, as downstream sectors are reliant on inputs from
sectors further up the value chain. A demand shock on the other hand should propagate
from downstream sectors to upstream ones, as their sales of inputs are directly tied to the
demand for the nal product. Here, it is also interesting to compare the impact through the
global value chain with the "own" impact on the sector. Our demand shock is represented
by changes in all government sectors' expenditure weighted by the share of sales of each
sector i to the government, whereas the TFP shocks are lagged changes of estimated fourfactor total factor productivity.
The results reported in the last two columns of Table 2 provide support to the upward
propagation of demand shocks (government spending), whereas results for supply (TFP)
shocks are inconclusive. However, we should remark that the supply shock regression
utilises a smaller sample because of lack of data for TFP, both cross-sectionally and time
wise.
ECB Working Paper 2064, May 2017
17
6
Conclusions
As we have shown in this paper, the global economy is a network of complex input-output
linkages characterised by large sectoral hubs. Our ndings conrm the statistical and
economic signicance of these links for transmitting economic activity across sectors in the
global economy. Our estimates suggest that a 1% change in economic activity in a sector's
global value chain translates into around 0.3 percentage points impact on the activity of the
sector, on average. We also provide evidence that it is not input-output linkages per se that
cause the spillovers, but rather the presence of large hub sectors in the global economy that
tie otherwise unrelated sectors together. In the absence of these sectors, spillovers through
the global value chain become signicantly reduced. This highlights their importance in
synchronising economic activity across the global economy.
When assessing the transmission of sectoral shocks in the global network, we can conrm
that demand shocks propagate upwards through the global value chain whereas results for
supply shocks (TFP) are ambiguous. The eect stemming from these shocks through the
value chain are fairly large, whereas the "own" impact is small and sometimes insignicant.
This suggests that exogenous shocks only have a moderate direct impact on a sector,
whereas the impact transmits and propagates through the global value chains, via the hub
sectors.
We therefore add to the growing empirical literature (Saito, Nirei and Carvalho, 2014;
di Giovanni, Levchenko and Mejean, 2014; Acemoglu, Akcigit and Kerr, 2015; Boehm,
Flaaen, Pandalai-Nayar, 2014 and Auer, Levchenko and Sauré, 2017) on the importance
of input-output linkages for movements in aggregate activity. The ndings also stress the
importance for policy makers not to only focus on aggregate - or global - shocks when
considering cross-country spillovers, but also to take into account international production
linkages. Moreover, we can conrm that the network structure of global production matters
for how economic shocks might transmit through the presence of hub sectors, as suggested
by Acemoglu, Carvalho, Ozdaglar and Tahbaz-Salehi (2012) and Carvalho (2014).
Some caveats to the results in this paper should be highlighted. First, an obvious pitfall
is that our data is not "granular" enough to make valid statements about the sector-level
transmission of economic shocks. Ideally, we would like to test the hypothesis of rm-level
spillovers in global value chains and their impact on aggregate activity. However, rm-level
data is scarce and rm-level input-output data even more so. While not perfect, analysis
ECB Working Paper 2064, May 2017
18
on less aggregated input-output tables for the United States, as in Acemoglu, Akcigit and
Kerr (2015) still nd robust results with more nely disaggregated sectors.
In addition, our empirical model does not capture substitution of suppliers in the face
of large disruptions, especially within sectors, which is one valid critique to input-output
tables in general. While valid, the few studies that have attempted to estimate substitution
eects between rms nd that they are fairly small at least in the short term (see for
example, Boehm, Flaaen, Pandalai-Nayar, 2014).
An interesting avenue for future research would be to estimate substitution eects in
the longer run and investigate the speed of substitution with non-linear eects. In addition, rm-level evidence on the transmission of economic activity through complete global
input-output networks (as in the World Input-Output database) and the identication of
global "hub" rms could yield a better understanding of cross-country spillovers driven by
granular shocks.
ECB Working Paper 2064, May 2017
19
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ECB Working Paper 2064, May 2017
22
Tables and Figures
Table 1: Moran I's statistics
year Moran I z-score p-value
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
0.088
0.136
0.202
0.165
0.099
0.070
0.068
0.076
0.052
0.002
0.003
0.092
0.002
0.004
0.137
0.082
27.27
41.96
62.21
53.15
31.94
25.77
22.66
26.71
18.04
1.52
4.46
35.70
2.97
2.26
50.07
31.50
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.064
0.000
0.000
0.002
0.012
0.000
0.000
Notes :
For each year, the table reports Moran I statistics (second column) and the test for the hypothesis H0 : no network
interdependence (third and fourth columns). For details on hypothesis testing, the reader can refer to Moran (1950).
ECB Working Paper 2064, May 2017
23
ECB Working Paper 2064, May 2017
24
n
17511
0.138***
(0.013)
0.156 ***
(0.015)
0.059***
(0.013)
y
17511
0.134***
(0.023)
0.238***
(0.008)
-0.037***
(0.013)
0.046***
(0.017)
0.028**
(0.013)
n
17511
0.114***
(0.023)
0.236***
(0.008)
- 0.024*
(0.014)
-0.028*
(0.016)
0.011
(0.024)
-0.005
(0.014)
-0.036***
(0.013)
0.049***
(0.017)
0.027**
(0.013)
unobs. factors
+ controls +
global bc
y
17511
-0.036***
(0.013)
0.002
(0.013)
0.020**
(0.009)
0.009
(0.008)
0.198***
(0.013)
0.239***
(0.008)
government
(demand)
shock
y
4950
0.058**
(0.028)
0.002
(0.015)
0.003
(0.015)
-0.034*
(0.023)
0.060**
(0.031)
0.206***
(0.015)
TFP (supply)
shock
The table reports estimated coecients from regression (1) where the dependent variable yit is the log dierence of value added. The average of the dependent
variables is considered as common factor in the error term. To make it possible to compare coecients, variables are standardized and the coecient reported
measure the eect of a one standard deviation change of the independent variables. Standard errors are reported in brackets.
Notes : ∗ ∗ ∗p < 0.01, ∗ ∗ p < 0.05, ∗p < 0.1
year eects
obs.
interest rate
metal
fuel
agriculture
employment
country
own
downstream
upstream
lag
baseline
unobs.factors
+ controls
Table 2: Regression results
ECB Working Paper 2064, May 2017
25
downstream 1997
DEU - transport equipment
downstream 2009
USA - basic metals and fab- FRA - transport equipment
ricated metal
JPN - construction
USA - transport equipment
USA - electrical and optical CHN - construction
equipment
DEU - basic metals and fab- DEU - basic metals and fabricated metal
ricated metal
CHN - electrical and optical
equipment
CHN - basic metals and fabricated metal
GBR - renting of m&eq and USA - public admin and de- USA - public admin and defence; compulsory social se- fence; compulsory social seother business activities
curity
curity
DEU - basic metals and fab- USA - construction
DEU - construction
ricated metal
USA - nancial intermedia- DEU - machinery, nec
DEU - machinery, nec
tion
DEU - renting of m&eq and DEU - transport equipment
other business activities
USA - renting of m&eq and USA - transport equipment
other business activities
RUS - mining and quarrying DEU - construction
upstream 2009
FRA - renting of m&eq and
other business activities
RUS - wholesale trade and
commission trade, except of
motor vehicles and motorcycles
USA - nancial intermedia- NLD - renting of m&eq and
tion
other business activities
USA - wholesale trade and DEU - chemicals and chemcommission trade, except of ical
motor vehicles and motorcycles
RUS - wholesale trade and
commission trade, except of
motor vehicles and motorcycles
DEU - chemicals and chemical
RUS - coke, rened
petroleum and nuclear
fuel
RUS - mining and quarrying
DEU - basic metals and fabricated metal
USA - renting of m&eq and
other business activities
DEU - renting of m&eq and
other business activities
RUS - inland transport
upstream 1997
Table 3: Ranking of sectors in the production network - real value added
Top sectors according to number of presences in other sectors' function
Table 4: Change in value added of important hub sectors
1% change to value added growth
Upstream
Downstream
Germany:
China:
Renting of machinery and
equipment and other
business activities
Electronics and optical
equipment
number of sectors
aected
321
172
sum of impact
across aected
sectors
1.14
0.47
of which is locally:
0.56
0.19
of which is in the
euro area:
0.40
0.07
of which is
cross-country:
0.18
0.21
Origin of the
change
∗
Notes : The impact ofPsector j reported in the columns on each other sector i is computed as ρ∗ wij,t
and the
∗
∗
overall impact as ρ∗ j6=i 1(wij,t
≥ r∗ )wij,t
with local (same country) and cross-country eects calculated
by considering the aected sectors. * stands for "up" and "down".
Figure 1: Stylised network representations
Source : Acemoglu, Carvalho, Ozdaglar and Tahbaz-Salehi (2012) "The Network Origins of Aggregate Fluctuations"
ECB Working Paper 2064, May 2017
26
Figure 2: The weighted degree distribution across sectors
Note :
The gure shows the sum over all the weights of the network in which a sector and is a direct and indirect inputsupplying or purchasing sector in 2009. Sources: WIOD and authors' calculations.
Figure 3: Weighted degree and global value added
Note : The Figure plots each country-sectors % share of global value added (x-axis) against the same sectors weighted degree
(y-axis). Sources: see Figure 2.
ECB Working Paper 2064, May 2017
27
Figure 4: Network distance and correlations across distance for upstream and downstream
sectors
(left-hand panel: average distance, right-hand panel: correlation coecient)
Note :
The left-hand panel of Figure 4 shows the shortest path length (number of edges) between country pairs computed
with the adjacency matrix assigning 1 if nonzero trade in intermediate between i and j , 0 otherwise from the respective
Input-Output matrix. Transaction below 100,000$ have been considered as 0. The shortest path has been computed with
the Dijkstra algorithm. For each country, average (upstream and downstream) distances from all country-sector linkages,
excluding sectors in the own country, are reported. The right-hand panel shows the average (1996-2009) pairwise correlation
between sectors' value added, at given distance to upstream and downstream sectors.
Sources: WIOD (2013 and 2016 release) and authors' calculations.
Figure 5: Value added spillovers without upstream and downstream hubs
(estimates of ρup and ρdown )
Note :
The gures show the estimated coecient from "upstream" (left-hand panel) and downstream (right-hand panel) in
the second column of Table 6. "All sectors" is the exact entry in Table 6, whereas top 1 refer to estimates when the top 1
global sector is cancelled out, top 5 estimates without the top 5 global sectors and so on.
Sources: WIOD (2013 release) and authors' calculations.
ECB Working Paper 2064, May 2017
28
Appendices
A
Additional Results
Table 5: Correlation between upstream and downstream weights
year
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
simple
weights corr.
0.32
0.32
0.32
0.32
0.32
0.31
0.32
0.32
0.32
0.32
0.32
0.31
0.31
0.31
0.32
year dist corrected
weights corr.
1995
0.32
1996
0.32
1997
0.32
1998
0.32
1999
0.32
2000
0.31
2001
0.32
2002
0.32
2003
0.32
2004
0.32
2005
0.32
2006
0.31
2007
0.31
2008
0.31
2009
0.32
Notes :
For each year, correlation between upstream (equation (4)) and downstream (equation (3)) weights have been comdown are equal to one for any ij .
puted. “Simple weights” refers to the case in which dup
ij,t and dij,t
ECB Working Paper 2064, May 2017
29
ECB Working Paper 2064, May 2017
30
n
17511
0.027***
(0.012)
0.705***
(0.050)
0.407***
(0.051)
y
17511
0.152***
(0.027)
0.455***
(0.015)
-0.033***
(0.012)
0.185***
(0.069)
0.125**
(0.058)
n
17511
0.129***
(0.026)
0.453***
(0.015)
-0.056*
(0.032)
-0.030*
(0.017)
0.011
(0.023)
-0.078
(0.226)
-0.032***
(0.012)
0.198***
(0.069)
0.123**
(0.058)
unobs. factors
+ controls +
global bc
y
17511
-0.033***
(0.012)
0.307
(1.671)
1.330**
(0.626)
0.060
(0.054)
0.224***
(0.015)
0.456***
(0.015)
government
(demand)
shock
y
4950
0.038*
(0.021)
0.001
(0.007)
0.004
(0.022)
-0.036*
(0.024)
0.099**
(0.043)
0.457***
(0.033)
TFP (supply)
shock
The table reports estimated coecients from regression (1) where the dependent variable yit is the log dierence of value added. The average of the dependent
variables is considered as common factor in the error term. Standard errors are reported in brackets.
Notes : ∗ ∗ ∗p < 0.01, ∗ ∗ p < 0.05, ∗p < 0.1
year eects
obs.
interest rate
metal
fuel
agriculture
employment
country
own
downstream
upstream
lag
baseline
unobs.factors
+ controls
Table 6: Regression results - Full sample (1997-2009)
ECB Working Paper 2064, May 2017
31
n
14817
0.121***
(0.015)
0.201***
(0.016)
0.067***
(0.014)
y
14817
0.104***
(0.026)
0.176***
(0.008)
0.146***
(0.009)
-0.068***
(0.015)
0.062***
(0.019)
0.037***
(0.014)
n
14817
0.090***
(0.026)
0.175
(0.008)
0.145***
(0.008)
-0.027*
(0.015)
-0.029*
(0.015)
0.022
(0.025)
-0.010
(0.017)
-0.067***
(0.015)
0.065***
(0.019)
0.036**
(0.014)
unobs. factors
+ controls +
global bc
y
14817
-0.067***
(0.015)
0.087***
(0.016)
0.013
(0.013)
-0.002
(0.009)
0.188***
(0.015)
0.177***
(0.008)
0.149***
(0.009)
government
(demand)
shock
y
4950
0.029
(0.029)
0.002
(0.015)
0.002
(0.015)
-0.01
(0.023)
0.051*
(0.031)
0.182***
(0.015)
0.092***
(0.017)
TFP (supply)
shock
See notes to Table 6. To make it possible to compare coecients, variables are standardized and the coecient reported measure the eect of a one standard
deviation change of the independent variables. Standard errors are reported in brackets.
Notes : ∗ ∗ ∗p < 0.01, ∗ ∗ p < 0.05, ∗p < 0.1
year eects
obs.
interest rate
metal
fuel
agriculture
capital
employment
country
own
downstream
upstream
lag
baseline
unobs.factors
+ controls
Table 7: Regression results - 1997-2007 sample - standardized coecients
ECB Working Paper 2064, May 2017
32
n
14817
0.119***
(0.015)
0.662***
(0.052)
0.246***
(0.052)
y
14817
0.118***
(0.029)
0.375***
(0.018)
0.454***
(0.026)
-0.062***
(0.013)
0.251***
(0.075)
0.165***
(0.064)
See notes to Table 6. Standard errors are reported in brackets.
Notes : ∗ ∗ ∗p < 0.01, ∗ ∗ p < 0.05, ∗p < 0.1
year eects
obs.
interest rate
metal
fuel
agriculture
capital
employment
country
own
downstream
upstream
lag
baseline
unobs.factors
+ controls
n
14817
0.102***
(0.029)
0.371***
(0.018)
0.448***
(0.026)
-0.066*
(0.038)
-0.034*
(0.018)
0.027
(0.031)
-0.209
(0.367)
-0.062***
(0.013)
0.262***
(0.075)
0.161**
(0.064)
unobs. factors
+ controls +
global bc
y
14817
-0.062***
(0.013)
17.318***
(3.190)
1.282
(1.250)
-0.027
(0.108)
0.213***
(0.017)
0.376***
(0.018)
0.461***
(0.026)
government
(demand)
shock
y
4950
0.025
(0.024)
0.001
(0.007)
0.003
(0.022)
-0.011
(0.025)
0.075*
(0.045)
0.400***
(0.034)
0.230***
(0.042)
TFP (supply)
shock
Table 8: Regression results - 1997-2007 sample - non-standardized coecients
Table 9: Change in value added of important hub sectors - 1997-2007
sample
1% change to value added growth
Upstream
Downstream
Germany:
China:
Renting of machinery and
equipment and other
business activities
Electronics and optical
equipment
number of sectors
aected
305
154
sum of impact
across aected
sectors
1.39
0.53
of which is locally:
0.69
0.22
of which is in the
euro area:
0.42
0.08
of which is
cross-country:
0.28
0.23
Origin of the
change
∗
Notes : The impact ofPsector j reported in the columns on each other sector i is computed as ρ∗ wij,t
and the
∗
∗
overall impact as ρ∗ j6=i 1(wij,t
≥ r∗ )wij,t
with local (same country) and cross-country eects calculated
by considering the aected sectors. * stands for "up" and "down".
ECB Working Paper 2064, May 2017
33
B
Computational Details
For each t = 1995, ..., 2009
- N C - total number of countries
- N I - total number of sectors
- n = N C × N I total number of country-sectors
- Y - (N C ∗ N I × 1) vector of country-sector real value added (e.g. element yi is the
real value of German car industry). Nominal gross value added deated with value
added price index.
- Z - n × n global input-output matrix. Element zij is the amount of intermediate
goods produced in sector i used in sector j 's production. Reading the matrix along
a column yields the intermediate goods produced in all sectors used in a particular
sector. A particular row provides information on the intermediate goods from a
particular sector to all global value chains in the world.
- GO - n × n diagonal matrix with sectors gross output on the diagonal
- A = ZGO−1 n × n technical coecient matrix
- L = (I − A)−1 n × n Leontief matrix
- v - n×n diagonal matrix with value added vector on the diagonal. Value added vector
contains sectors share of direct domestic value added in total output. This is equal
to one minus the intermediate input share from all countries (including domestically
produced intermediates).
- V A = v L GO value added contribution matrix. Reading the matrix along the
column, yields the value added produced in all sectors used in a particular sector.
Each row provides information on the value added from a particular sector to all
ECB Working Paper 2064, May 2017
34
global value chains in the world.
V A = vLGO


v1 0 · · · 0
 0 v2 · · · 0  


=  .. .. . .

 . .

.
0 0 · · · vn

v1 L11 go1
0

0
v2 L22 go2

= 
.
..
..

.
0
0

L11 L12 · · · L1n

L21 L22 · · · L2n 



..
.. . .
.
. ..  
.
.
Ln1 Ln2 · · · Lnn

···
0

···
0


...

· · · vn Lnn gon

0
0 


...

· · · gon
go1 0 · · ·
0 go2 · · ·
..
.
..
.
0
0
- V A_w = V A GO−1 weighted (by total output) value added contribution matrix
- V A_outdegree =
- V A_indegree =
Pn
j=1,j6=i
Pn
i=1,i6=j
V A_wij (row-sums of V A_w)
V A_wij (column-sums of V A_w)
- V A_totdegree = V A_outdegree + V A_indegree
- Adj - nxn matrix with Adjij = 1 if Zij 6= 0 and Adjij = 0 if Zij = 0. Transaction
below 100,000$ have been considered as 0.
- Distance_up - n × n matrix with distances from upstream sectors. Its element dij is
the distance of sector i from the upstream sector j . Distance is computed from Adj ,
with the Dijkstra algorithm which nds the shortest path (number of edges) between
two sectors (nodes).
- Distance_down - n × n matrix with distances from downstream sectors. Its element
dij is the distance of sector i from the downstream sector j . It is the transposed of
Distance_up.
- W u - upstream value added weight matrix. Each element wij is obtained as wij =
V Ai→j /
Pn
i=1,i6=j
V Ai→j (value added contribution to j from i divided by total value
added contribution from all sectors i - column sums)
- W d - downstream value added weight matrix. Each element wij is obtained as wij =
V Ai→j /
Pn
j=1,j6=i
V Ai→j (value added contribution from i to j divided by total value
added contribution from i to all sectors j - row sums)
ECB Working Paper 2064, May 2017
35
Acknowledgements
We wish to thank Marta Banbura, Chris Boehm, Chiara Osbat, Stephanie Schmitt-Grohe, Yongcheol Shin, Georg Strasser and Máté
Tóth for useful comments and suggestions.
Erik Frohm
European Central Bank, Frankfurt am Main, Germany; email: [email protected]
Vanessa Gunnella
European Central Bank, Frankfurt am Main, Germany; email: [email protected]
© European Central Bank, 2017
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ISSN
ISBN
1725-2806(pdf)
978-92-899-2786-4 (pdf)
DOI
EU catalogue No
10.2866/489819(pdf)
QB-AR-17-076-EN-N(pdf)